To meet the rising performance and efficiency demands on high performance thermal management systems, this paper proposes a hierarchical model-based control framework for thermal-fluid power flow systems. This hierarchy uses scalable graph-based dynamic models of the hydrodynamics and thermodynamics of these systems, derived from conservation of mass and conservation of thermal energy, respectively. Leveraging the inherent timescale separation between thermal and hydraulic dynamics, a three-layer control hierarchy is constructed. The use of Model Predictive Control (MPC) at each layer allows actuator and state constraints to be explicitly considered and allows preview of upcoming thermal disturbances to be used for optimization. In addition, the hierarchy has functionality to account for actuator dynamics, including rate limits and time delays. The proposed control approach is demonstrated in simulation on a system configuration that is notionally representative of a simplified aircraft fuel thermal management system.